Falsetto singing may be defined as singing beyond upper normal range in a false voice elongating the vocal cords while closing the glottis (though it can be done in normal/ low notes as well). It is surprising to know that actually it is a Western concept, in early days churches didn't allow females to participate in singing hence they had castrated males singing in false voices hence called falsetto.
In Hindi music this was started by Kishore da. Actually Kishoreda's elder brother Anoop kumar had a great collection of Western classicals & songs, one day while entering the home he was angered when he heard someone singing in falsetto thinking that Kishore da is playing his records, but he was surprised to find that Kishore da was singing in falsetto voice.
S D Burman da used to call it gala tod ke gana & introduced it into Bollywood.
All of you must have heard the song Chala jata hoon by Kishoreda from Mere Jeevan saathi ( RD Burman), it is amazing to note how Kishoreda throws his voice up in antaara using falsetto.
It is surprising to notice that falsetto singing is not popular & practiced a lot by female singers but I'll mention one example.
In antaara of kajra re from Babli aur Bunty Alisha has used falsetto to increase her upper range.
In current singers Sonu Nigam has a fancy for it, he has used it in O mama from RHTDM, he uses it quite often otherwie as well.
Can you give me more examples........😊